Question

Find the number of selections taking at least one out of 5 similar white balls, 6 similar green balls, 7 similar red balls and 8 distinct blue balls.

• A.
• B.
• C. - 1
• D. - 1

Answer 1

The correct option is D

- 1

Number of ways of selecting 5 similar white balls = Selecting zero white balls or Selecting one of white balls or Selecting white balls Selecting all 5 similar white balls.

Number of ways of selecting 5 similar white balls = (5 + 1) ways = 6 ways

Similarly,

Number of ways of selecting 6 similar green balls = (6 + 1) ways = 7 ways

Number of ways of selecting 7 similar red balls = (7 + 1) ways = 8 ways

The number of selections 8 distinct blue balls =

Selecting zero blue balls out of 8 = ${}^8{C}_0$

Selecting 1 blue balls out of 8 = ${}^8{C}_1$

Selecting 2 blue balls out of 8 = ${}^8{C}_2$

.

.

.

.

Selecting all 8 blue balls = ${}^8{C}_8$

Sum of all these cases = ${}^8{C}_0$ + ${}^8{C}_1$ +${}^8{C}_2$ .......... + ${}^8{C}_8$ = $2^8$

Total number of ways = $6\times 7\times 8\times 2^8$

Since, we need to select at least one ball

So, remove the case when we are not selecting any ball

Total number of ways selecting at least one ball =$6\times 7\times 8\times 2^8$ - 1